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CARBON DIOXIDE SEQUESTRATION:WHEN AND HOW MUCH?
KlausKeller�, Zili Yang
�, Matt Hall
�, andDavid F. Bradford
��� ��� ��
Departmentof Geosciences,
ThePennsylvaniaStateUniversity,
UniversityPark,PA, 16802-2714,[email protected],
phone:(814)865-6718,fax: (814)865-7823.�Departmentof Economics,SUNY at Binghamton.�
BrookingsInstitution.�Woodrow Wilson Schoolof PublicandInternationalAffairs,
PrincetonUniversity�Departmentof Economics,PrincetonUniversity.�
Schoolof Law, New York University.
Center for EconomicPolicy Studies(CEPS)Working Paper No. 94
Princeton University
September2003
Abstract
We analyzecarbondioxide (CO� sequestrationasa strategy to managefuture climatechangein an
optimal economicgrowth framework. We approachthe problemin two ways: first, by usinga simple
analyticalmodel,andsecond,by usinga numericaloptimizationmodelwhich allows us to explore the
problemin amorerealisticsetting.CO� sequestrationis notaperfectsubstitutefor avoidingCO2 produc-
tion becauseCO2 leaksbackto theatmosphereandhenceimposesfuturecosts.The“efficiency factor”of
CO2 sequestrationcanbeexpressedastheratio of theavoidedemissionsto theeconomicallyequivalent
amountof sequesteredCO2 emissions.A simpleanalyticalmodelin termsof anet-presentvaluecriterion
suggeststhatshort-termsequestrationmethodssuchasafforestationcanbesomewhat( � 60 %) efficient,
while long term sequestration(suchasdeepaquiferor deepoceansequestration)canbe very ( � 90%)
efficient. A numericalstudyindicatesthatCO2 sequestrationmethodsatacostwithin therangeof present
estimatesreducetheeconomicallyoptimalCO2 concentrationsandclimaterelateddamages.Thepotential
savingsassociatedwith CO2 sequestrationis equivalentin our utilitarian modelto a one-timeinvestment
of severalpercentof presentgrossworld product.
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1 Intr oduction
Anthropogenicgreenhousegas emissionsare projectedto changefuture climatesand to causenon-
negligible economicdamages[Munasingheet al., 1996; Weyant et al., 1996]. Efforts to mitigate the
greenhousegasproblemhave traditionally focusedon avoiding the productionof carbondioxide (CO2)
by reducingfossil fuel use(typically referredto as“CO2 abatement”)[Nordhaus, 1992;Tol, 1997]. One
alternative to CO2 abatementwould beto captureCO2 emissionsandsequesterthemin carbonreservoirs
suchasdeepaquifers,deepoceans,or minerals[Lackneret al., 1995;Herzog andDrake, 1996;Hoffert
et al., 2002]. However, large-scalesequestrationpresentsconsiderablescientific,engineering,andeco-
nomicproblems.Oneeconomicproblemis thatCO2 sequestrationis not a perfectsubstitutefor avoiding
CO2 production.This is becausesequesteredCO2 mayleakbackinto theatmosphereandimposefuture
climatedamages.In contrast,avoidingCO2 productionwouldnot imposethelegacy of CO2 leakage.
Whetheror notCO2 sequestrationshouldbeconsideredasaviablealternative to CO2 abatementis an
openandmuchdebatedquestion[Kaiser, 2000]. PreviousstudiesaddressingCO2 sequestrationdevelop
elegantanalyticalexpressionsto analyzethetradeoff betweenCO2 sequestrationandCO2 abatement(e.g.,
Richards [1997], vanKootenet al. [1997], Herzog et al. [2003]) or analyzetheoptimaluseof CO2 se-
questrationin numericalmodels(e.g., Swinehart[1996],Biggsetal. [2000],LecocqandChomitz[2001]).
While breakingimportantnew ground,thesestudiesaresilentonimportantpolicy questions.For example,
theanalyticalmodelstypically neglect thefeedbackeffectscausedby theavailability of theCO2 seques-
trationtechnologyonfuturecarbontaxes.Also, mostnumericalmodelsfocusonafforestation(whichcan
only playaminor role in reducingclimatechange[NilssonandSchopehauser, 1995;Adam, 2001]).Stud-
ies analyzingmorepowerful sequestrationmethods( ������ , deep-oceanor deep-aquiferinjection) assume
negligible marginal costs[Nordhaus, 1992],neglectcostreductionsastechnologiesmature,[Biggset al.,
2000;Herzog et al., 2003]),or neglectCO2 leakage[Ha-DuongandKeith, 2002].
Herewe expandandimproveon thepreviouswork in two respects.First,we refineandapplyanana-
lytical model[Richards, 1997]by estimatingtherelevantmodelparametersandestimatingtheefficiency
factorof CO2 sequestration.Second,weexpandanoptimaleconomicgrowth model[NordhausandYang,
1996]by addingCO2 sequestration,learning-by-doing,andtechnologicalinertia. We usethenumerical
modelto analyzetheoptimaluseof CO2 sequestrationmethodsandtheeffectsof optimal carbondiox-
ide levels. Specifically, we askfive questions:(i) What is the tradeoff (or the ratio of marginal benefits)
betweenCO2 sequestrationandCO2 abatement?(ii) What is the optimal useandtiming of sequestra-
tion? (iii) How doesCO2 sequestrationchangethe optimal tax path? (iv) How do technologicalinertia
andendogenouslearningaffect theoptimaluseof sequestration?and(v) What is thepresentvalueof a
technologythatwouldprovidesequestrationin thefuture?
We proposeaneconomicframework to measuretheefficiency of CO2 sequestration.Specifically, we
estimatethenetpresentvalueof sequesteredCO2, in termsof avoidedabatementcosts,to meeta specific
atmosphericconcentrationconstraint. CO2 sequestrationcanreplacecostly abatementmeasuresin the
2
presentandhencehasaneconomicvalue. However, leaky CO2 sequestrationimposesfuturecosts.The
net savings ( ���� �� , the initial savings minus the future costs)relative to the initial savings representsthe
efficiency factorof CO2 sequestration.Theresultsfrom our analyticalmodelsuggestthatafforestationis
somewhatefficient ( � 60%),while long-termsequestrationpossibilities,suchasdeepaquifersequestra-
tion or oceaninjection,couldbequiteefficient ( � 90%).
The analyticalmodel providesan intuitive andsimple methodto accountfor future leakageof se-
questeredcarbon.Thesimplicity of theanalyticalmodelneglects,however, severalpotentiallyimportant
effectssuchashyperbolicdiscounting[Weitzman, 1998]or learning-by-doing[ArgoteandEpple, 1990].
We addresstheseshortcomingsby analyzinga numericaloptimalgrowth model.Our numericalanalysis
suggeststhat theavailability of a viablesequestrationtechnologycanlower carbontaxesandtheoptimal
atmosphericCO2 concentrations.In the model,CO2 sequestrationat marginal costswithin the rangeof
presentestimatesis deployed in increasingvolumeto sequesterall the industrialCO2 emissionsby the
middle of the next century. Learning-by-doingandtechnologicalinertia createan “R & D” market for
earlysequestration,beforeit is competitivewith abatementtechnologies.Learning-by-doingallowssoci-
ety to “buy-down” thepriceof sequestrationby employing the technologyearlier. Technologicalinertia
requiresearlier sequestrationto achieve large-scalequantitative goalsin the next century. The poten-
tial economicbenefitsderivedfrom sequestrationareseveralpercentof present-daygrossworld product
(GWP).Theresultsof our analysisaresensitive to severalparameters,suchastherateat which learning-
by-doingoccurs,the maximumrateat which a new technologycanpenetratethe market, or the rateof
carbonleakage.
2 The efficiencyfactor of CO2 sequestration:
A simpleanalytical model
Theefficiency factorfor CO2 sequestrationis asimplemeasureto analyzetheeconomictradeoff between
CO2 abatementandCO2 sequestration.In anoptimalpolicy, differentCO2 control technologiesareused
suchthattheirmarginalsocialvalue(shadow price)areequalized.Thus,in aworld in whichsequestration
hasa constantefficiency, � , relative to that of abatement,and an optimal tax ( � ) is levied on all CO2
emissions(includingthosethataresequestered),theoptimal“refund” leviedfor eachtonCO2 sequestered
shouldbeequalto theproduct ����� . As therelative efficiency of sequestrationapproachesunity (perfect
substitutefor abatement),the refundapproachesfull reimbursement.Conversely, in a credit regime for
sequestration,thefractionof a full creditcorrespondingto thefractionof thesocialvalueof abatement,� ,
shouldbegivenfor eachton sequestered.
Givenits importance,thefirst goalof ouranalysisis to derivetheefficiency factorof CO2 sequestration
to comparesequesteredcarbonwith avoidedcarbonemissions.For example,100tonsof sequesteredCO2
wouldoffset50tonsof avoidedCO2 emissionsatanefficiency factorof 50%. To illustratethestructureof
3
theproblem,westartwith asimpleanalyticalmodel,similar to theonedevelopedby Richards[1997]. We
expandontheanalysisof Richards[1997]by estimatingrelevantparametersandby deriving ananalytical
expressionfor the economicefficiency of carbonsequestrationconsidering(i) discounting,(ii) changes
in futurecarbontaxes,(iii) leakage,and(iv) anenergy penaltyof carbonsequestration.As we illustrate
in thesubsequentsection,many conclusionsderivedfrom this simplemodelarevalid in a morerealistic
numericalmodel.
The tradeoff betweenCO2 abatementandCO2 sequestrationis affectedin our analyticalmodelby
four factors:(i) theadditionalenergy requirement;(ii) theCO2 leakageover time; (iii) thechangesover
time in marginal abatementcosts;and(iv) thediscountrate. In thefollowing sectionwe developsimple
closedform solutionsto representthesefactorsandderive anexpressionfor theefficiency factorof CO2
sequestration.For analyticalconvenience,weapproximatetheproblemby aninfinite horizonproblem.
The first factoraccountsfor the energy requirementof CO2 sequestration.The additionalenergy is
derivedby burningmorefossil fuel andthusimposesan“energy penalty”. Therelative “energy penalty”
( � is the consequenceof the energy-intensive natureof capturing,transporting,andsequesteringCO2
emissions.� is definedastherelative increasein fossil fuel usedueto CO2 captureandsequestration.The
relative increasein CO2 emissionsthatmustbe sequesteredto yield thesameamountof energy for end
useis: ���� � � (1)
Somefractionof thesequesteredCO2 will leakbackto theatmosphere.We approximatethe leakageby
anexponentialdecayof thesequesteredCO2 stock.Theleakageflux of on ton of CO2 over time ( � �!� � is
thena functionof thedecayrate( " andtheenergy penalty( � :� �#� %$ "�&� � ('*),+.- (2)
where� startsat thetimeof sequestration.
For theanalyticalmodel,we assumeanagreeduponatmosphericCO2 stabilizationpath. Associated
with this stabilizationpathis apathof allowableCO2 emissions.Themarginal CO2 abatementcostsover
time arethena function of theCO2 reductionsover time andthe availableabatementtechnologieswith
their associatedmarginal costs.If we think abouttheCO2 stabilizationpathasimplementedby theappli-
cationof anemissionstax, this carbontax would follow thesamepathasthemarginal abatementcosts,
in this stylizedexample.For theagreeduponCO2 stabilizationpath,any leakagehasto becompensated
by increasedabatement.BecauseCO2 abatementis costly, CO2 leakageimposesadditionalcostsin the
future.Theadditionalcostsareapproximated— in apartialequilibriumsense— by thecarbontax times
theleakageflux.
We estimatefuture carbontaxesby fitting a simpleexponentialfunction to resultsfrom an optimal
growth model. We usetheRICE model[NordhausandYang, 1996] to estimatecarbontaxesthatcorre-
4
spondto an optimal emissionspathsubjectto atmosphericconcentrationstabilizationtargets. For CO2
stabilizationtargetsbetween450ppmand750ppm,theconstraintoptimalcarbontaxesarewell approx-
imatedfor the next two centuriesby exponentialfunctions. The carbontaxesover time ( /10 ) arehence
approximatedas: /102�#� 3$5476 98:+;- (3)
where 476 is the initial carbontax in U.S.$per ton of C and 4 is the carbontax growth rate. Note that
theoptimalabatementcostsat themargin areequalto theoptimalcarbontax giventheassumedperfect
markets. Thecarbontaxesareprojectedto increaseover time mostlybecausethepositive marginal pro-
ductivity of capitalaswell asthefreeserviceof thenaturalcarbonsinksfavor laterabatementmeasures.
Thelastassumptionrequiredfor theanalyticalmodelis to discountfuturecostsby adiscountfactor( < ),
<��!� =$ ('?>@+;- (4)
whereA is thediscountrate.
Deriving theefficiency factorof a leaky CO2 sequestrationprojectis now anexerciseof calculatingthe
netpresentvalueof theprojectandrelatingit to thecostsof thealternative choiceof carbonabatement.
Technically, the net benefitof sequesteredCO2 at time zero is the avoided carbontax ( 476 ), minus the
presentvalueof futurecostsimposedby theCO2 leakage.Thenetbenefitspertonof CO2 sequesteredcan
beexpressedby:
netbenefit $5476 � +CB7DE+CB 6 ('?>@+ 476 98F+ "��� � ('*),+G<��H- (5)
which canbesolvedanalyticallyfor A�IJ" � 4LKNM . (Otherwise,thecostsof leakagegrow fasterthanthe
rateat which they arediscountedandthepresentvaluesumof costswill exceedall benefitsderivedfrom
thetonof sequesteredCO� .) Thesolutionfor thenetbenefitis:
netbenefit $O476 � ��� "�!A�IP" � 4Q � �&� � � (6)
The expressionin parenthesesreducesthe initial projectbenefitat no leakage(the marginal abatement
costsat the time of sequestration)andcanbe interpretedasan “efficiency factorof CO2 sequestration”.
Wehencerewrite equation(6) as:
� $ netbenefitinitial carbontax
$ � ��� "�RASIP" � 4Q � ��� � - (7)
where � is the efficiency factorof sequestrationcalculatedby the ratio of net benefitfrom a CO2 unit
sequesteredto the net benefitof a CO2 unit of avoided emissions. Note that the efficiency factor of
5
sequestrationis alsoequalto theratio of themarginal benefitsof sequestrationto themarginal benefitsof
abatementin theadoptedoptimalgrowth framework.
This simple efficiency model is a stylized representationof the complex interactionsbetweense-
questrationandhumanwelfare. However, sucha framework maybe preferableto alternative weighting
schemesthat measureefficiency in termsof carbonthat neglect issuessuchasthe marginal productiv-
ity of capitalor CO2 leakagebeyond an arbitrarily chosentime horizon[Fearnsideet al., 2000; Costa
and Wilson, 2000]. Although this analyticalmodel givesus someinsight into the economictradeoffs
involved with CO2 sequestration,it hasseveral shortcomings.First, the partial equilibrium assumption
implicit in the fixed carbontax path is only reasonablefor very small-scaleuseof CO2 sequestration.
This is becauselarge-scaleCO2 sequestrationwould affect the carbontax pathwhich we assumeto be
unaffected.Second,ouranalyticalmodelneglectsmechanismssuchashyperbolicdiscounting[Weitzman,
1998],backstoptechnologies[ManneandRichels, 1991],or technologicalinertia [Grubler et al., 1999].
Weshallanalyzetheseeffectsin themorerealisticnumericalmodeldevelopedbelow.
3 The optimal useof CO2 sequestration:
An optimal growth model
We usetheRegional IntegratedModel of ClimateandtheEconomy(RICE) [NordhausandYang, 1996]
asa startingpoint. This optimalgrowth modellinks theglobal climateandeconomicsystemby simple
feedbacks.Thecurrentmodelversion(RICE-01)differsfrom theoriginalRICE-96[NordhausandYang,
1996] model in two ways. First, we have updatedthe model parametersto be consistentwith recent
work Nordhausand Boyer [2000]. Second,we modify the model to accountfor carbonsequestration,
technologicalinertia, and learning-by-doing.In the following sectionswe give a brief overview of the
model structureand how we incorporatecarbonsequestration,technologicalinertia, and learning-by-
doing.
3.1 The RICE model
TheRICEmodellinks climaticrelationshipsbetweenatmosphericCO2 concentrationandnetglobalradia-
tive forcing to economicrelationshipsbetweenconsumptionandinvestmentin capital. TheRICE model
aimsto maximizethediscountedsumof utility derivedfrom generalizedconsumptionover a giventime
horizon.
The economiccomponentof the RICE model is a Ramsey type modelof economicoptimal growth
[Ramsey, 1928]. In theRamsey model,asocialplannerchoosespathsof consumption( T ) andinvestment
to maximizeanobjective function UWV . In theRICE model,theobjective function is theweightedsumof
thenaturallogarithmof per-capitaconsumptionwith theweightingfactorspopulationlevel ( X ), a factor
6
accountingfor the“pure rateof socialtimepreference”Y , andthe“time-variantNegishiweights” Z :
U V $ [\(] +_^\+CB 6 Z`�Rab-c� edgf � T��Rab-c� X&�RaQ-�� X&�!ab-�� � � IhY '?+i� (8)
TheNegishiweightsareaninstrumentto accountfor regionaldisparitiesin economicdevelopment.They
equalizethemarginalutility of consumptionin eachregionfor eachperiodin orderto preventlargecapital
flowsbetweenregions.This techniqueis descriptiveratherthanprescriptive;althoughthechoiceof utility
functionimpliesthatsuchcapitalflowswouldgreatlyimprovesocialwelfare,without theNegishiweights
theproblemof climatechangewould bedrownedby thevastly largerproblemof underdevelopment.A
detailedexpositionof Negishi weightsis given in Nordhausand Yang [1996] and the referencescited
therein.
In thisequation,theterm dgf �jlk] � +Cmn k] � +Cm representstheflow of utility at time � for region a andthesumma-
tion occursfrom somestartingpoint � $oM to a finite time horizon � V . Thefinite time horizonis required
by thenumericalsolutiontechnique.It is, however, just a numericalapproximationto aninfinite horizon
problemasusedin theanalyticalmodel(equation5). Thefinite time horizonis chosensuchthattheend
point hasno significanteffecton thepolicy decisionin theanalyzedtime frame.
Investment( p ) in capitalis specifiedin themodelasthebalanceof output( q ) that is not devotedto
consumptionin agiventimeperiod:
qr�RaQ-�� 3$ Tr�!ab-�� Ispl�Rab-c� � (9)
Investmentcontributesto the capitalstock( t ) of the next period,which thendepreciatesat a constant
proportionalrate( u over time:
ts�RaQ-��vI � =$ � �w� u ts�!ab-�� Ihpl�!ab-�� � (10)
At eachpoint in time, thecapitalstockandlaborsupply(which is exogenouslyspecified)influencegross
world product.In RICE, this relationshipis expressedby a modifiedCobb-Douglasfunction:
qx�!ab-�� 3$5y �Rab-c� z �!ab-�� ts�RaQ-�� .{ X&�RaQ-�� � ' { � (11)
In the model, grossworld output dependson exogenouslyand endogenouslyevolving elements. The
exogenouselementsare the multi-factorproductivity ( z ), the populationlevel, and the constantshare
of capital ( | in the economy. The endogenouslydeterminedelementsarecapitalanda scalingfactor
( y� , which accountsfor the costsfrom investingin carbonmitigation technologiesandclimate-related
damages,asdiscussedbelow.
The economicandthe naturalsystemsarelinked in the modelby the anthropogenicCO2 emissions
7
( } ). The CO2 emissionsdependon the economicoutput, the exogenouslydeterminedenergy-intensity
of GWP ( ~ , the CO2 abatementrate ( � ), and the exogenouslyevolving land-useCO2 emissions( � )
accordingto: }x�!ab-�� 3$ ~3�RaQ-�� q��!ab-�� �� ��� �=�Rab-c� i� Ih�x�RaQ-�� � (12)
Without carbonmitigation the carbonemissionsfollow a baseline“businessasusual” (BAU) scenario.
IncreasingrelativeCO2 abatementimposesincreasingrelativeabatementcosts( � ):
�x�Rab-c� %$5�9� �Ra �3�RaQ-�� �!� k]mi- (13)
with �9� �Ra and ��� �Ra beingmodelparameters.CO2 emissionsact to increasetheatmosphericCO2 stock
(M � + . However, increasedCO2 concentrationsin the atmospheredrive someproportioninto the upper
ocean(M � � . Eventuallymostof a givenCO2 pulseemittedinto theatmosphereis absorbedby thedeep-
ocean(M ��� accordingto afirst-orderlinearmodeldefinedby:
� � + �!�@I � =$ \�] }r�RaQ-��,I � I �9�.� � � + �!� I �H��� � �c�*�#� - (14)
� � �*�#�vI � =$��9�R� � � + �#� I ���.� � � �?�!� I �H�.� � �����!� - (15)
and � �����!�@I � 3$5�H�.� � �c�*�#� I ���.� � �����!� � (16)
Thevariables��� � � aretheentriesin thecarboncyclemodeltransitionmatrix [NordhausandBoyer, 2000].
AtmosphericCO2 levelsabove thepreindustriallevel of 590Gigatonsof carboncausea netradiative
greenhousegasforcing ( � ): ���!� 3$5� � � dgf,� � � + �!� �h�(� M(���=d_f ��� - (17)
wherethe factorof 4.1 is thechangein radiative forcing dueto a doublingof atmosphericCO2 concen-
trations. Note that physicalvariables,suchasthe atmosphericCO2 stockor temperature,areall global
in themodel. As such,temperaturechangein themodelis really thetemporalandspatialaverageof the
changein globalsurfacetemperature.Increasedradiative forcing is translatedinto globalmeantempera-
turechange�!� by asimpleclimatemodel:
���!� =$ ���#� �N� I �R~ �c�� ���!� � �¢¡£���#� �N� � �R~ � �#���!� �N� � � V �!� �¤� ci� � (18)
In this equation�¥9¦ denotesthethermalcapacityof theoceanicmixedlayerand � ¡ is theclimatefeedback
parameter. Theclimatesensitivity ( ��V ) of themodelis definedastheequilibriumtemperatureresponseto
adoublingof atmosphericCO2. Theclimatesensitivity is givenby � V $¨§x© ��ªi«�¬ � , where®¯� �;° j7± � is the
radiative forcing causedby a doublingof CO2. Theparameter~ � representstheratio of theheatcapacity
8
of thedeepoceanto transferratefrom theoceanicmixedlayer to thedeepocean. �²V is thedeviation of
thedeep-oceantemperaturefrom thepreindustriallevel approximatedby:
� V �!� =$ � V �#� �N� I �R~ � �!���!� �¤� � � V �#� �N� ci� � (19)
To completethecircle linking climateto theeconomy, temperaturechanges( � , equation18) causeeco-
nomicdamages( ³ ), which arespecifiedasa fractionof thegrossworld product:
³´�RaQ-�� 3$ µ¶� �Ra ���!� I µ·� �Ra ���!� � � (20)
Thecostsof carbonmanagementandthe climatedamagesaresubtractedfrom thegrossworld product,
therebydeterminingthescalingfactor y :
y �!ab-�� %$ ��� ³´�!ab-�� � ���RaQ-�� � (21)
3.2 Representationof CO2 Sequestration
We addsequestrationasanadditionalcarbonmanagementoption to thestandardabatementoptioncon-
sideredin the original RICE-01 model. The carbonsequestrationflux ( ¸ ) is removed from industrial
emissions( } � � ) andstoredin a carbonreservoir (M >.¹ from which it leaksbackinto theatmosphere
following anexponentialdecay:
� >.¹ �!�@I � =$ \ ] ¸&�!ab-��@I � I � �.� � >.¹ �!� � (22)
All sequesteredcarbonis presumedin this exerciseto enterthe samereservoir; this is mathematically
equivalentto anarbitrarynumberof reservoirs for our assumptionof a linearrateof decay. Theoriginal
equationdescribingtheatmosphericCO2 budget(14) is hencemodifiedas:
� � + �#�,I � =$ \(] � }x�!ab-��@I � � ¸��!ab-��@I � .� I �9�.� � � + �!� I ����� � � �*�!� I � � � � >.¹ �!� � (23)
Sequestrationis representedasa carbonbackstoptechnology, similar to the representationof non-
abatementoptionsin previous economicmodels( ������ , Ward [1979], Manneet al. [1995]). A backstop
technologyimplies that the marginal costsof sequesteringCO2 canbe approximatedasindependentof
thesequesteredquantity. This somewhatcrudeapproximationmight be justifiedbecausethecapacityof
carbonsequestrationmethods(suchasinjection into deepaquifers,the deepoceans,or CO2 absorption
out of theatmosphere)exceedsthenecessaryCO2 emissionreductions[Elliot et al., 2001;Herzog et al.,
2001;Ha-DuongandKeith, 2002].NotethattheCO2 sequestrationmethodbasedon CO2 absorptionout
of the air [Lackner, 2003] is a very closeapproximationto the type of backstoptechnologyconsidered
9
here,as the marginal costsareratherinsensitive to the fraction of anthropogenicCO2 emissionsbeing
sequestered.
In themodel,wesubtracttheproductof theCO2 sequestrationflux andthemarginalsequestrationcosts
( ºr�!� ) from world output.Theoriginalproductionfunction(equation11) is hencemodifiedaccordingto:
q��!ab-�� =$ y �Rab-c� z �!ab-�� ts�RaQ-�� .{ X&�RaQ-�� � ' { � ¸��RaQ-�� º��!� � (24)
Sequestrationbecomesanadditionalchoice(besidesCO2 abatementandcapitalinvestment)to maximize
the objective function. We neglect the possibility that CO2 sequestrationmight occurout of the atmo-
sphere.As a result,sequestrationfluxeshave to bebelow theindustrialemissions.
Presentestimatesof themarginal costsof CO2 sequestrationvary widely andareprimarily basedon
theoreticalcalculations.Giventheconsiderabletechnologicalandlogisticalchallengesof largescaleCO2
sequestration,the cost estimateshave to be taken with a grain of salt. Williams [2003], for example,
considersanintegratedgasificationcombinedcyclepowerplantusingcoal.For hydrogenproduction,the
marginal costof CO2 sequestrationis estimatedasroughly50U.S.$pertonC. For electricityproduction,
theestimatedmarginalcostsarearound100U.S.$pertonC.For comparison,ChiesaandConsonni[2000]
analyzenaturalgas-firedcombinedcycle power plantsandestimatesthat carbontaxesbetweenroughly
125to 180U.S.$perton C would rendertheCO2 sequestrationoptioncompetitive. We adopta marginal
costfor large scalecarbonsequestrationof 100 U.S.$per ton C asour centralestimateandexplore the
implicationsof this parameteruncertaintyin asensitivity study(discussedbelow).
3.3 Representationof Learning-by-Doing
Technologicalimprovementsresultingfrom large-scalemanufactureof varioustechnologieshave been
shown to decreasethe costsof thosetechnologiesin a phenomenontypically referredto as “learning-
by-doing” [ArgoteandEpple, 1990]. Learning-by-doingis especiallyimportantfor relatively new tech-
nologiessuchasCO2 sequestration.To representlearning-by-doingfor CO2 sequestration,the costof
sequesteringoneton of carbondioxide ( º ) decreasesin our modelasa functionof cumulative installed
capacity( 00 ) accordingto: 0�0(�!�@I � =$ 0�0(�!� I \�] ¸��!ab-�� � (25)
and ºr�#� 3$ º 6�� 00(�!� 002�#� 6H � '*»2� (26)
Notethattheaboveequationimpliesthatcumulativecapacityis irrespectiveof theregion in whichtheca-
pacityis installed,meaningthatcost-reducingtechnologiesdevelopedin eachregionareperfectlyshared.
10
Thecostcurve is characterizedby anexponent( ¼ ) thatis a functionof the“progressratio” (½¢A ):
¼ $ � dgf �¾½7A dgf �¿� � (27)
The progressratio is definedasthe relative costsafter a doublingof the installedcapacity. We assume
a progressratio of 85% to representtechnologiesbetweenthe researchanddevelopmentphaseandthe
commercializationphase[Grubler et al., 1999]. As initial installedcapacity, we assume10 Gt C to
representa relatively immaturetechnology.
Introducinglearning-by-doingcanintroducelocal maximainto theunderlyingoptimizationproblem
[Messner, 1997]. Basically, the technologiescanbe trappedin a local basinof attractionif the existing
maturetechnologyis cheaperthanthenew (but initially moreexpensive) technology. The local maxima
canseverelylimit theappliedlocalsearchalgorithmimplementedin GAMS/MINOS[Brookeetal., 1998].
We testwhetherthesolutionis a local (asopposedto a global)solutionby startingthemodelsimulations
at differentinitial conditionsfor abatementandsequestrationsfor thebasecase.The fact thatall model
simulationsconverge to basicallythe sameresultarguesstronglyagainstthe existenceof relevant local
maximain theobjectivefunction.Themodelis formulatedin GAMS [Brookeetal., 1998]andis available
from theauthors.
3.4 Representationof TechnologicalInertia
Market penetrationratesof new technologiesarelimited by factorssuchascapitalturnover or diffusion
of knowledge.Thepenetrationratesof technologiessuchasnaturalgas,cars,or oil canbeapproximated
asan exponentialincreaseof deliveredquantity [Grubler et al., 1999]. Thusa constantmaximumal-
lowablegrowth rateseemsan appropriateconstraintto prevent the obviously unrealisticstrategy of an
instantaneousscale-upof sequestration.An instantaneousscale-upwould imply infinite penetrationrates,
inconsistentwith theobservations.
Historical ratesof market penetrationcanbe quite high. For example,thegrowth rateof the energy
suppliedby gashasbeenaround7.5 % per year in the U.S. over the last 150 years(seeGrubler et al.
[1999]). However, becauseof theextensive infrastructurenecessaryfor large-scalecarbonsequestration,
it seemsmoreappropriateto compareit to otherinfrastructure-intensive technologies(suchasrailroads),
which requiremoretime to penetratethemarket. For this reasonwe choosea growth constraintof 5 %
per year for carbonsequestrationin our model. The increasein CO2 sequestrationover time is hence
constrainedby amaximumallowablegrowth rate( À :¸��!ab-��@I � :Á � � IPÀ ¸��Rab-c� � (28)
Thegrowth constraintfor CO2 sequestrationgivenabove is region-specific.Thus,while costreductions
11
from technologicaladvancescanbesharedbetweenregions,the increasesin capacityto sequesteremis-
sionscannot: eachregion must investtime andresourcesinto the necessaryinfrastructureto sequester
CO2.
4 Resultsand Discussion
4.1 Analytical Model
We first examineresultsderivedfrom theanalyticalmodel(equation7) to illustratesomegeneralproper-
tiesof theproblem.As aninstructiveexample,considertheefficiency factorof afforestation.We choose
economicparametervalueswhich approximatetheoptimalpolicy in theRICE model,resultingin a dis-
count rateof 5 % year' �anda carbontax growth rateof 1.5 % year' �
(consistentwith concentration
stabilizationat 650 ppm). We further assumea half-life time of carbonin newly plantedforestsof 40
years,andan energy penaltyof 10%. This yields an efficiency factorof 61%. For comparison,deep
aquifersequestration(assuminga half-life time of 1000yearsandanenergy penaltyof 15%)would have
anefficiency factorof morethan95%.
Thissimplemodelsuggestsfour mainconclusions.First,ahigherdiscountrateincreasestheefficiency
factorby lesseningthepresent-valuecostsassociatedwith futureleakage.Second,ahigherenergy penalty
decreasestheefficiency factorby anincreasein overall energy production.Third, smallerreservoir half-
life times(equivalentto larger leakagerates)decreasetheefficiency factorby allowing carbonto escape
sequestrationearlier(Figure1). And fourth,ahighercarbontaxgrowth ratedecreasestheefficiency factor
by increasingthecostof cuttingemissionsto compensatefor leakedCO2.
4.2 Optimal EconomicGrowth Model
Theanalyticalmodelis usefulto expressthetradeoff betweensequesteredandabatedCO2 emissionsin a
closedform solution.Thesimplicity of theanalyticalmodelcomes,however, at thepricethatthesystem
hasto be extremelysimplified. For example,the analyticalmodelneglectsthe effectsof (i) learning-
by-doing, (ii) hyperbolicdiscounting,(iii) technologicalinertia, and (iv) the availability of the carbon
backstoptechnologyonoptimalcarbontaxes.Weusethenumericalmodelto analyzetheseeffects.
The first questionwe addresswith the numericalmodel is how the availability of the CO2 seques-
tration technologyaffectsoptimal carbontaxes. To isolatethis effect, we useexponentialdiscounting,
neglect the technologicalinertia constraintsand learning-by-doing.CO2 sequestrationis availableat a
constantmarginal costof 100U.S.$perton C anda reservoir half-life time of 200a. Theoptimalcarbon
taxesfor this simulationin thecasewithout sequestration,with perfectsequestrationandwith a “leaky”
sequestrationareshown in Figure2.
12
0 200 400 600 800 10000
10
20
30
40
50
60
70
80
90
100
reservoir half−life time [year]
sequ
estr
atio
n ef
ficie
ncy
(η)
in %
r=2% a−1
r=3.6% a−1r=7% a−1
Figure1: Relationshipbetweenthe reservoir half-life time of a sequestrationprojectand its efficiencyfactor( � ) (equation7 in thetext) for differentdiscountrates( A ).
In this example, the optimal carbontax increasesin all threecasesin the next 150 yearsand ap-
proachesthemarginal costsof carbonsequestration.If carbonsequestrationis not available,thecarbon
tax continuesto rise. If a perfectbackstoptechnologysuchasnon-leakingcarbonsequestrationwithout
a technologicalinertiaconstraintis available,thecarbontaxesareboundby thebackstopprice(equalto
100U.S.$perton C in this example).
Sequestrationactshereasa backstoptechnologyby forcing themarginal costof abatementto remain
below a flat price. In the casewhereCO2 sequestrationis the perfectsubstitutefor abatement( �c�£ �� , no
leakage),societyis indifferentbetweenthe two technologiesassoonasthemarginal costsof abatement
andsequestrationareequal( ���� �� , at theintersectionof theabatementcostscurvewith theflat sequestration
costcurveat100U.S.$pertonC shown in Figure2). In thecasewhereCO2 sequestrationresultsin future
CO2 leaks,it is not a perfectsubstitutefor abatement.As a result,leaky CO2 sequestrationis only used
at a highercarbontax thanthemarginal costof thetechnology. SinceCO2 sequestrationis not a perfect
substitutefor abatement,it is worth lessin theoptimalgrowth framework, andthepriceat which carbon
sequestrationis usedexceedsthe marginal costsof $100per ton. In fact, the ratio of the marginal cost
of sequestrationto themarginal costof abatementwhenbothareusedrepresentstheefficiency factorof
sequestrationintroducedbefore. Reassuringly, the estimatedsequestrationefficienciesagreequite well
betweenthe analyticaland the numericalmodel. (The valuesare 78 to 86% in the numericalmodel
comparedto 84%in theanalyticalmodelusingthesamemodelparameters.)This impliesthattheoptimal
choicebetweenCO2 sequestrationandCO2 abatementin thissimplifiedexampleis well approximatedby
theanalyticalefficiency factorderivedin equation(7).
13
2000 2050 2100 2150 2200 22500
20
40
60
80
100
120
140
160
180
carb
on ta
x [$
per
ton]
year
no sequestrationperfect sequestrationleaky sequestration
Figure2: Theeffect of CO� sequestration(with andwithout CO� leakage)on optimalcarbontaxes. Seetext for details.
We now analyzetheeffectsof hyperbolicdiscounting,learningcurves,andtechnologicalinertia. Our
modelsuggeststhattechnologicalinertia,hyperbolicdiscountingandlearning-by-doingall actto increase
theoptimaluseof carbonsequestrationin thenearfuture(Figure3).
In this simulation,two phenomenaaredriving earlieruseof sequestration.First, employing the rel-
atively new technologyof CO2 sequestration,reducesthe futuremarginal costs.This effect is moreim-
portantfor relatively new technologies.Second,sequesteringcarbonin smallamountsearlyonallowsthe
scaleup in time to achievesequestrationof all industrialemissionsearlyin thenext century(Figure3).
Theintroductionof sequestrationtechnologiescandramaticallyreducetheoptimalatmosphericcon-
centrationof CO2, dependingon themarginal costof CO2 sequestration(Figure4).
With a relatively expensiveCO2 sequestrationtechnology(for example150U.S.$perton C) CO� se-
questrationis not usedandthe atmosphericCO2 concentrationsexceed750 ppmV in 2250. For a CO2
sequestrationcostof 100U.S.$per ton C (thecentralestimate),CO� sequestrationis usedandthepeak
of theoptimalCO2 trajectorydecreasesto lessthan550ppmV(Figure4). Thesecondaryincreasein CO2
concentrationin thelong run (Figure4A) is dueto therelatively early leakageof sequesteredCO2 at the
200yearreservoir half-life time. For a 2000yearreservoir half-life time, theoptimalCO2 concentrations
donotshow thissecondaryincrease(Figure4B).NotethattheoptimalCO2 pathsfor arguablyrealisticas-
sumptionsaboutpresentCO2 sequestrationcostscanbeconsiderablylower thanpreviousoptimalgrowth
analyses( ����l� , Tol [1997]or NordhausandBoyer[2000]).
Cheaperclimatecontrolstrategiescanimprovetheweightedsumof presentandfuturewelfares(equa-
tion 8) by reducingthemarginalcontrolcosts.In anoptimalgrowth framework, reducedmarginalcontrol
14
2000 2050 2100 2150 2200 22500
5
10
15
20
[GtC
per
yea
r]
year
productionemissionssequestrationabatement
2000 2050 2100 2150 2200 2250−8
−6
−4
−2
0
2
4
6
8
[GtC
per
yea
r]
year
sinksleakage∆ atmosp.
Figure 3: Optimal carbonfluxes over time for the basecase. The simulationsassume(i) hyperbolicdiscounting,(ii) a technologicalinertiaconstraint,(iii) learning-by-doing,(iv) aninitial CO2 sequestrationcostof 100 U.S.$per ton C, and(v) a reservoir half-life time of 200 years.The emissionsin the upperpanelincludetheCO2 emissionsdueto land-usechanges(equation12). Seetext for details.
costsresultin reducedglobalwarming(Figure5a)and,in turn, in reducedclimatic damages.
CO2 sequestrationcan hencebe a valuabletechnology. We usethe optimal growth framework to
estimatethe economicvalueof the sequestrationoption asa function of initial price andreservoir half-
life time (Figure5b). Thevalueof theCO2 sequestrationtechnologyis estimatedby theamounta social
plannerwould bewilling to pay todayfor a sequestrationtechnology. Thevalueof a CO2 sequestration
technologyis high whensequestrationis relatively cheap,nearly6 % of present-dayGWPat $50U.S.$
perton C anda reservoir half life time of 200years.In otherwords,a budgetof 6 % of presentGWP(as
a onetime investment)to successfullydevelopa CO2 sequestrationtechnologyat a marginal costof $ 50
U.S.$pertonC andareservoir half life timeof 200yearswouldpassacost-benefittestin ourmodel.The
valueof CO2 sequestrationtechnologiesincreaseswith cheaperoptionsandwith longerreservoir half life
times.
15
2000 2050 2100 2150 2200 2250300
400
500
600
700
800
half life time 200 years
atm
osph
eric
CO
2 [ppm
v]
A
year
150 $/tC100 $/tC80 $/tC50 $/tC20 $/tC
2000 2050 2100 2150 2200 2250300
400
500
600
700
800
B
half life time 2000 years
atm
osph
eric
CO
2 [ppm
v]
year
150 $/tC100 $/tC80 $/tC50 $/tC20 $/tC
Figure4: OptimalCO� trajectoriesasa functionof initial CO� sequestrationcostsandreservoir half-lifetime. Theupperpanel(A) assumesa reservoir half-life timeof 200years.Thelowerpanel(B) assumesahalf-life timeof 2000years.
Thebenefitsof CO2 sequestrationwould justify asubsidyfor this technologyin theoptimaleconomic
growthmodel.Thisis illustratedin themarginalCO2 abatementcostsfor CO2 sequestrationandabatement
alonganoptimalpath(Figure6).
In thisexample,CO2 sequestrationis usedevenif it is (initially) moreexpensivethanCO2 abatement.
Theuseof themoreexpensiveCO2 sequestrationoptionis justifiedbecausethelearning-by-doingreduces
the unit costsfor the relatively new technology. In this example, it is optimal to subsidizeearly CO2
sequestration.
In Figure6, sequestrationis usedearlyon, eventhoughit is initially moreexpensive thanabatement.
Suchusedrivesdown thecostof futureCO2 sequestrationwhile capacityrampsup by themaximumrate
at which new technologiescanpenetratethe market (equation28). Around the year2150,the capacity
for CO2 sequestrationis largeenoughthatessentiallyall industrialemissionscanbesequestered.By then
16
2000 2050 2100 2150 2200 22500
1
2
3
4
5
year
tem
pera
ture
Cha
nge
[o C]
A
150 $/tC100 $/tC50 $/tC20 $/tC
0 50 100 1500
2
4
6
8
10
12
14
16
initial price of sequestration
valu
e of
tech
nolo
gy [%
199
5 G
WP
]
B 200 years reservoir half−life2000 years reservoir half−life
Figure5: Effect of differentinitial CO2 sequestrationcostson optimaltemperaturechangesandthevalueof thesequestrationtechnology. Shown aretheoptimaltemperaturechangesfor half-life timeof 200years(upperpanel,A). Thelower panel(B) givesthevalueof CO2 sequestrationtechnologiesasa functionofinitial priceandreservoir half-life time.
sequestrationtechnologieshave maturedin the model to the point that cost reductionsfrom increased
cumulative capacityare small, andwe get the relationshipthat we would expect betweenthe price of
sequestrationandthepriceof abatementasderivedin ouranalyticalmodelandillustratedin Figure2. The
ratio of thesemarginal costsis the marginal economicefficiency of sequestrationrelative to abatement.
Clearly, early sequestrationefforts are quite valuablein this example. In the nearterm, the marginal
sequestrationcostsareabove the marginal abatementcostsasspecifiedby the initial conditionsin the
model. In the optimalpolicy, the marginal costsfor theoptimaluseof CO2 declinedueto learning-by-
doing. In thelong run, themarginal costsfor optimalCO2 sequestrationfall below themarginal costsfor
optimal CO2 abatementbecauseleaky CO2 sequestrationis inefficient (dueto leakage)andhencehasa
lowershadow valuethanCO2 abatement(similar to Figure2).
17
2000 2050 2100 2150 2200 22500
10
20
30
40
50
60
70
80
90
100
year
mar
gina
l cos
t [$
per
ton]
sequestrationabatement
Figure6: Marginal costsfor CO� sequestration(stars)andCO� abatement(circles)for an initial seques-trationpriceof 100U.S.$perton C.
5 Caveats
Our analysisis subjectto considerableparameteruncertaintyandtheresultsare— of course— sensitive
to thechosenparameters.Weexploresomeeffectsof parameteruncertaintyby asimplescenarioanalysis.
(Notethatthisapproachstill assumesperfectknowledgewithin eachscenario).Weexaminethesensitivity
of theoptimalCO2 trajectorieswith respectto thetechnologicalinertia,theprogressratio,andthepresent
experiencein CO2 sequestration.This sensitivity analysissuggeststhat the modelconclusionsarevery
sensitiveto theconstraintontechnologicalinertiaandtheprogressratio,butarelesssensitiveto thepresent
experiencein CO2 sequestration(Figure7). It is somewhatreassuringthatthealternativechoicesof model
parametersshown in Figure7 do not considerablyaffect theoptimaltrajectoriesof CO2 andcarbontaxes
over thenext few decades.
Our modelsasnothingmorethanthinking tools to analyzethe interactionsof the socialandnatural
systemin a consistentway. Importantlimitationsof our analysisincludethe limited treatmentof uncer-
tainty andthecrudeapproximationsof thenaturalandeconomicsystem.Finally, it is importantto recall
two of our main assumptions.(i) CO2 sequestrationis both availableandsafein large quantities;(ii)
Decisionsarebasedon adiscountedutilitarian framework.
18
2000 2050 2100 2150 2200 2250350
400
450
500
550
600
650A
CO
2 con
cent
ratio
n [p
pm]
base casepr=75%pr=95%
2000 2050 2100 2150 2200 22500
50
100
150
carb
on ta
x [$
per
ton
C]
Bbase casepr=75%pr=95%
2000 2050 2100 2150 2200 2250350
400
450
500
550C
CO
2 con
cent
ratio
n [p
pm]
base casecc=20 GtCcc=5 GtC
2000 2050 2100 2150 2200 22500
50
100
150
carb
on ta
x [$
per
ton
C]
D
base casecc=20 GtCcc=5 GtC
2000 2050 2100 2150 2200 2250
400
500
600
700
800
E
CO
2 con
cent
ratio
n [p
pm]
year
base caseα=7% per aα=3% per a
2000 2050 2100 2150 2200 22500
50
100
150
year
carb
on ta
x [$
per
ton
C]
Fbase caseα=7% per aα=3% per a
Figure7: Sensitivity studywith respectto therepresentationof theprogressratio (panelsA andB, param-eterpr, asdefinedin equation27),theinitial installedcumulativebaseof CO� sequestration(panelsC andD, parametercc, asdefinedin equation25),andthetechnologicalinertia(panelsE andF, parameterÀ , asdefinedin equation28). Eachsensitivity studycomparesthebasecasewith a high andlow valuefor theparameterin question.
6 Conclusions
Ouranalysissuggeststhreemainconclusions.First,theanalysisof thenetpresentvalueof CO� sequestra-
tion yieldsanexpressionfor theefficiency factorwhich seemspreferableto previouscarbonaccounting
methods.Second,a subsidyfor the initially noncompetitive technologyof CO2 sequestrationcanbe a
soundeconomicpolicy. Subsidiesfor CO2 sequestrationcanhelp to overcometechnologicalinertia, to
reducemarginal costsvia learning-by-doing,andto increasepercapitaconsumption.Third, andfinally,
CO2 sequestrationpresentsapotentiallow-costsolutionto thegreenhousegasproblem.CO2 sequestration
couldreducemitigationcostsandclimatedamagesconsiderably.
19
Acknowledgments Financialsupportfrom theCarbonMitigation Initiative at PrincetonUniversityandtheEn-
vironmentalConsortiumat PennStateis gratefullyacknowledged.We aregratefulto S. Pacala,M. Oppenheimer,
R. Socolow, andB. Williams for helpful discussions.Any remainingmistakesaresolely the responsibilityof the
authors.
20
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